Solve Second Order ODE: Find a Values for Zero Tendency

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Homework Statement



Find all values of a for which all solutions of

y''(x) + (a/x)y'(x) + (5/2)y(x) = 0

tend to zero as x tends 0+ and all values for which all solutions tend to zero as x tends to +

Homework Equations


The Attempt at a Solution



I am not even sure where to being with this problem. My guess is to examine all cases for b-(a2/4). Just not really sure on this at all.
 
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You should know the http://math.colgate.edu/~wweckesser/math311/handouts/second_order.pdf" to a second-order differential equation to solve this.

Then look at the possible solutions based on what you have for a and x.
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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